# ---
# title: 858. Mirror Reflection
# id: problem858
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Math
# link: <https://leetcode.com/problems/mirror-reflection/description/>
# hidden: true
# ---
# 
# There is a special square room with mirrors on each of the four walls.  Except
# for the southwest corner, there are receptors on each of the remaining
# corners, numbered `0`, `1`, and `2`.
# 
# The square room has walls of length `p`, and a laser ray from the southwest
# corner first meets the east wall at a distance `q` from the `0`th receptor.
# 
# Return the number of the receptor that the ray meets first.  (It is guaranteed
# that the ray will meet a receptor eventually.)
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: p = 2, q = 1
#     Output: 2
#     Explanation: The ray meets receptor 2 the first time it gets reflected back to the left wall.
#     ![](https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/18/reflection.png)
#     
# 
# **Note:**
# 
#   1. `1 <= p <= 1000`
#   2. `0 <= q <= p`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
